OFFSET
0,4
COMMENTS
1/sqrt((1-x)^2-4rx^3) expands to sum{k=0..floor(n/2), binomial(n-k,k)binomial(n-2k,k)r^k}
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..2309
Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
FORMULA
a(n)=sum{k=0..floor(n/2), binomial(n-k, k)binomial(n-2k, k)2^k}. D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Nov 10 2014
MATHEMATICA
Array[Sum[Binomial[# - k, k] Binomial[# - 2 k, k] 2^k, {k, 0, #/2}] &, 29, 0] (* Michael De Vlieger, Jul 16 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 10 2004
STATUS
approved